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Chapter 1: Q. 9 (page 135)

Write the difference rule for limits in terms of delta–epsilon statements.

Short Answer

Expert verified

The difference rule for limit is

limx→c[f(x)-g(x)]=limx→cf(x)-limx→cg(x).

Step by step solution

01

Step 1. Given information.

We need to write the difference rule limx→c[f(x)-g(x)]=limx→cf(x)-limx→cg(x)in terms of delta-epsilon statement.

02

Step 2. Proof.

For all ε>0, there exists δ>0such that if 0<|x-c|<δ.

Then,

[f(x)-g(x)]-(L-M)<εf(x)-g(x)-L+M<ε

where L=limx→cf(x)and

M=limx→cg(x).

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